Problem: Simplify the following expression: $ q = \dfrac{2}{k - 8} + 7 $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{k - 8}{k - 8}$ $ \dfrac{-7}{1} \times \dfrac{k - 8}{k - 8} = \dfrac{-7k + 56}{k - 8} $ Therefore $ q = \dfrac{2}{k - 8} - \dfrac{-7k + 56}{k - 8} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{2 - (-7k + 56) }{k - 8} $ Distribute the negative sign: $q = \dfrac{2 + 7k - 56}{k - 8}$ $q = \dfrac{7k - 54}{k - 8}$